Underground drilling, such as gas, oil, or geothermal drilling, generally involves drilling a bore through a formation deep in the earth. Such bores are formed by connecting a drill bit to long sections of pipe, referred to as a “drill pipe,” so as to form an assembly commonly referred to as a “drill string.” The drill string extends from the surface to the bottom of the bore.
The drill bit is rotated so that the drill bit advances into the earth, thereby forming the bore. In rotary drilling, the drill bit is rotated by rotating the drill string at the surface. Piston-operated pumps on the surface pump high-pressure fluid, referred to as “drilling mud,” through an internal passage in the drill string and out through the drill bit. The drilling mud lubricates the drill bit, and flushes cuttings from the path of the drill bit. In the case of motor drilling, the flowing mud also powers a drilling motor, commonly referred to as a “mud motor,” which turns the bit, whether or not the drill string is rotating. The mud motor is equipped with a rotor that generates a torque in response to the passage of the drilling mud therethrough. The rotor is coupled to the drill bit so that the torque is transferred to the drill bit, causing the drill bit to rotate. The drilling mud then flows to the surface through an annular passage formed between the drill string and the surface of the bore.
The drilling environment, and especially hard rock drilling, can induce substantial vibration and shock into the drill string. Vibration also can be introduced by rotation of the drill bit, the motors used to rotate the drill bit, the pumping of drilling mud, imbalance in the drill string, etc. Such vibration can result in premature failure of the various components of the drill string, premature dulling of the drill bit, or may cause the drilling to be performed at less than optimum conditions. For example, although reducing the downhole force applied to the drill bit, commonly referred to as the “weight on bit” (“WOB”) or the rotary speed of the drill bit may reduce vibration, it may also reduce drilling efficiency. In particular, drill bits are typically designed for a predetermined range of rotary speed and WOB and do not perform as effectively if operated outside this range in order to avoid excessive vibration. Moreover, operating the drill bit away from its design point can reduce the service life of the drill bit. Substantial vibration can even directly reduce the rate of penetration of the drill bit. For example, very high axial vibration can result in a loss of contact between the drill bit and the surface being drilled.
A drill string may experience various types of vibration. “Axial vibration” refers to vibration in the direction along the drill string axis. “Lateral vibration” refers to vibration perpendicular to the drill string axis. Lateral vibration often arises because the drill string rotates in a bent condition. Two other sources of lateral vibration are “forward” and “backward”, or “reverse”, whirl. “Whirl” refers to a situation in which the bit orbits around the bore hole in addition to rotating about its own axis. In backward whirl, the bit orbits in a direction opposite to the direction of rotation of the drill bit. “Torsional vibration,” also of concern in underground drilling, is usually the result of what is referred to as “stick-slip.” Stick-slip occurs when the drill bit or lower section of the drill string momentarily stops rotating (i.e., “sticks”) while the drill string above continues to rotate, thereby causing the drill string to “wind up,” after which the stuck element “slips” and rotates again. Often, the bit will over-speed as it unwinds.
In general, optimal drilling is obtained when the rate of penetration of the drill bit into the formation is as high as possible while the vibration is as low as possible. The rate of penetration (“ROP”) is a function of a number of variables, including the rotational speed of the drill bit and the WOB. During drilling, surface equipment senses the rate of penetration of the drill bit into the formation, the rotational speed of the drill string, the hook load, surface torque, and pressure. Sensors either at the surface or in a bottomhole assembly (“BHA”), or both, measure the axial tensile/compression load, torque and bending.
APS's SureShot™ Surface System
Systems currently on the market, such as APS Technology's SureShot™ surface system, receive and process information from sensors near the bit, such as WOB sensors, torque sensors, inclination sensors (i.e., accelerometers) and azimuth sensors (i.e., magnetometers), and transmit the information to other surface equipment. A surface estimate of WOB may also be derived from hook load and drag calculations. The SureShot™ system also receives data on the mud flow rate from other surface software. Typically, such software determines the mud flow rate from a curve provided by the mud pump supplier relating flow rate to stroke rate of the pump pistons, rather than from a direct flow rate sensors. In any event, using a curve of mud motor flow rate versus motor RPM or an RPM/flow rate factor, the surface software also determines the mud motor RPM. The SureShot™ system also calculates the build rate, normally expressed as degrees per 100 feet or degrees per 30 meters, based on the change in inclination measured by the accelerometers for the depth drilled. It also calculates the turn rate, normally expressed as degrees per 100 feet or degrees per 30 meters, based on the change in azimuth (i.e., the lateral direction of drilling) measured by the magnetometers. However, notwithstanding the availability of such data, obtaining the optimal rate of penetration is a difficult endeavor. Optimization of the drilling process is a constantly changing and ongoing process. Formations may change, bits may dull, mud weight and the hydraulics may change.
APS's Vibration Memory Module™
Systems currently on the market, such as APS Technology's Vibration Memory Module™, process data from accelerometers and magnetometers installed into the bottomhole assembly to determine the amplitudes of axial vibration, and of lateral vibration due to forward and backward whirl, at the location of these sensors. The Vibration Memory Module™ also determines torsional vibration due to stick-slip by measuring and recording the maximum and minimum instantaneous RPM over a given period of time, such as every four seconds, based on the output of the magnetometers. The amplitude of torsional vibration due to stick-slip is then determined by determining the difference between and maximum and minimum instantaneous rotary speeds of the drill string over the given period of time. Preferably, root-mean-square and peak values for the axial, lateral and torsional vibrations are recorded at predetermined intervals, such as every four seconds. The amplitudes of the axial, lateral and torsional vibration are transmitted to the surface via mud pulse telemetry.
Most systems, including the aforementioned Vibration Memory Module™, don't measure the frequency of the vibration, although some high end tools do. Insofar as the inventors are aware, none of the current tools, however, transmit the vibration frequency to the surface. However, when using the Vibration Memory Module™, burst data samples, recorded either as a result of the occurrence of an event or at preselected time periods, may be down loaded from the Vibration Memory Module™ after a run is completed and the BHA assembly is pulled out of the hole. Software at the surface can read the burst sample data, plot it and performs a Fourier analysis to determine the frequency of the vibration.
APS's Well Drill™
Other systems on the market, such as APS Technology's Welldrill™ system employ finite element techniques to predict the resonant frequencies and mode shapes associated with drill string vibration. The WellDrill™ system employs software that uses finite element techniques, in particular ANSYS software, to model the drill string based on the drill string geometry and mechanical properties. As shown in FIG. 1, the model is comprised of beam elements 53, connected by nodes 54, and contact elements 55. As shown in FIG. 2, the entire drill string 4—including a drill bit 8, mud motor 40, stabilizers 41, drill collars 43, Measurement While Drilling (“MWD”) tool 56—is modeled by a series of beam elements, nodes and contact elements. A beam element 53 is shown in FIG. 3A and comprises a uniaxial element with tension, compression, torsion, and bending capabilities. These elements have six degrees of freedom at each node: translations in the nodal x, y and z directions and rotations about the nodal x, y and z axes. Stress stiffening and large deflection capabilities are also included. The gaps between drill string components and the borehole are modeled using contact elements, each of which represents two surfaces which may maintain or break physical contact and may slide relative to each other. A contact element 55, shown in FIG. 3B, is capable of supporting only compression in the direction normal to the surfaces and shear (Coulomb) friction in the tangential direction, and have two degrees of freedom at each node: translations in the nodal x and y directions. Force and displacement constraints are applied to a node at each end of a drill string element and a contact element is attached to each node. The drill string is allowed to deflect laterally until it contacts the surface modeled by the contact element.
In particular, the WellDrill™ model of the drill string is created by entering data into the software to specify:                (i) the outside and inside diameters of the drill pipe sections that make up the drill string,        (ii) the locations of stabilizers,        (iii) the length of the drill string,        (iv) the inclination of the drill string,        (v) the bend angle if a bent sub is used,        (vi) the material properties, specifically the modulus of elasticity, material density, torsional modulus of elasticity, and Poisson's ratio,        (vii) the mud properties for vibration damping, specifically, the mud weight and viscosity,        (viii) the bore hole diameters along the length of the well obtained by adding an increment (e.g., 0.25 inch (6.4 mm)) to the diameter of the drill bit based on the type of formation,        (ix) the azimuth, build rate and turn rate,        (x) the diameter of the drill bit and stabilizers, and        (xi) information concerning the characteristics of the formation, such as the strike and dip. These are used when the formation is a non-homogenous material, having different compressive strengths in orthogonal directions.        
Strike is defined as the compass direction, relative to north, of the line formed by the intersection of a rock layer or other planar feature with an imaginary horizontal plane. The intersection of two flat planes is a straight line, and in this instance, the line is geologic strike. According to convention, the compass direction (or bearing) of this line is always measured and referred to relative to north. A typical bearing is given, for example, as N 45° E, which is a shorthand notation for a bearing that is 45° east of north (or half way between due north and due east). The only exception to this north rule occurs where strike is exactly east-west. Then, and only then, is a strike direction written that is not relative to north. Dip, as a part of the measurement of the attitude of a layer or planar feature, has two components: dip direction and dip magnitude. Dip direction is the compass direction (bearing) of maximum inclination of the layer or planar feature down from the horizontal and is always perpendicular (i.e., at a 90° angle) to strike. Dip magnitude is the smaller of the two angles formed by the intersection of the dipping layer or planar feature and the imaginary horizontal plane. However, dip magnitude can also be equal to either zero or 90°, where the layer or planar feature is horizontal or vertical, respectively.
From the data inputs specified above, the WellDrill™ software calculates the static deflection shape of the drill string so as to determine the points of contact between the drill string and the bore hole.
In addition, data are also entered into the WellDrill™ software specifying the expected operating parameters for (i) the WOB, (ii) the drill string RPM, (iii) the mud motor RPM, (iv) the diameter of the bore hole, and (v) the damping coefficient. The damping coefficient is calculated using a predetermined values of the viscosity of oil or water (depending on whether the operator indicates that an oil-based or water-based drilling mud is used), the density of the fluid (mud weight), and the annulus between the BHA and the bore hole. The bore hole diameter is estimated based on the diameter of the drill bit and the type of formation in lieu of not having caliper data. For example, if the formation is hard rock, the diameter of the bore hole may be estimated to be ½ inch larger than the diameter of the drill bit, whereas it may be estimated to be much larger than the drill bit for soft rock. (The maximum diameter is based on the number of cones or blades on the bit.) The diameter of the bore hole is also generally assumed to be bigger if a bent sub is used for rotary directional drilling.
As noted above, the WellDrill™ software performs static bending analysis to determine contact points between the drill string and the borehole. This provides support information for the vibration analysis. The static bending analysis determines the deflection, contact points, bending moments and the bending stress along the length of the drill string. The bending analysis is used to determine the predicted build and turn rate. The build rates are determined by a force balance at the drill bit. The critical speeds are determined by performing a forced harmonic frequency sweep. Excitation forces are applied at the bit and the power section of the mud motor. Wherever the excitation forces are near natural frequencies of the drill string, critical speeds occur.
In particular, the WellDrill™ software performs a forced response analysis by applying an oscillating WOB over selected range of WOBs and drill bit RPMs. The selected oscillating WOB is applied at two frequencies: (i) the rotary speed of the drill bit and (ii) the number of cones (for roller cone bits) or blades (for PDC bits) multiplied by the drill bit speed. Since mud motors rotors are eccentric by design, they always create an oscillating imbalance force, the magnitude of which is based on the rotor eccentricity and the frequency of which is equal to N(n+1), where n is the number of lobes on the rotor and N is the mud motor rotor RPM. Therefore, if a mud motor is used, the software includes in the forced response analysis an oscillating imbalance force based on the characteristics of the mud motor applied at frequencies based on a selected range of mud motor RPM. Typical drill string rotary speeds are 10-250 rpm, while mud motor speeds may be 50-250 rpm. The typical bit speed (combination of motor and rotary speeds) is, therefore, 60 to 500 rpm. Mud turbines operate at much higher speeds of 800-1500 rpm, but do not introduce a similar imbalance. Drill collars may also have features, such as electronics hatches, upsets and cutout, that create a rotating imbalance. In addition, drill collars that become bent in service create a rotating imbalance. Since such rotating imbalances are a source of vibration excitation, WellDrill™ can include them in the model.
Based on the foregoing, the WellDrill™ software predicts critical drilling speeds for the drill string, motor and bit. Critical speeds occur when the drilling forces excite the drill string such that the induced vibration causes damage to the drill string and/or results in lost drilling performance. Drilling forces that may excite the drilling and induce critical speeds include: bit forces from the blades or cones of the bit striking a discontinuity, bit whirling in an over gauge bore hole, the imbalance forces generated by the motor stator, imbalance forces from the drill string the drill string contacting the bore hole resulting in whirling, and under-gauge stabilizers whirling. Typically, when the frequency of the excitation force is at or near a natural frequency of the drill string, the displacement amplitudes are easier to excite. In addition, in severe drilling applications the excitation forces away from the natural frequencies may be severe enough to damage the drillstring and require their identification as critical speeds.
The WellDrill™ software also calculates the torque at each section along the drill string using the equation:T=θJG/L 
Where:                T=torque        θ=angular displacement        J=polar moment of inertia        G=shear modulus        L=length of the drill string section        
WellDrill™ uses the calculated torque to determine torsional vibrations by determining whether the torque applied to the drill bit is sufficient to rotate the drill string backward. If this condition is present then it is considered a torsional critical speed. WellDrill™ also uses the calculated torque to determine stick-slip conditions, in particular, whether the torque along the drill string is sufficient to overcome frictional resistance to rotation.
Stick-Slip Software
Software has also been used in the past to predict when stick-slip will occur using a finite difference technique. First, the software calculates the drag along the entire length of the drill string and at the bit. The calculation of drag is based on the methodology described in C. A. Johancsik et al., Torque And Drag In Directional Wells—Prediction and Measurement, Journal of Petroleum Technology, 987-992 (June 1984), herein incorporated by reference in its entirety.
The previously used stick-slip prediction software breaks up the drill string into finite lengths, typically less than thirty feet. The drag on each section is a function of the normal force the section exerts on the wall of the borehole and the coefficient of sliding friction between the drill string and the wall. The normal force is a function of the curvature of the drill string section, the tension in the section, and gravity effects. The coefficient of friction is primarily a function of the characteristics of the drilling mud and whether the borehole is cased or open. Its value can be empirically developed by, for example, applying the model to a drill string in which the pickup weight, slack-off weight and torque are measured to establish independent measurements of drag.
The software calculates the drag on each section of drill string as the incremental moment, ΔM, necessary to overcome the friction force, from the equations:ΔFn=[(FtΔα sin θA)2+((FtΔθ+W sin θA)2]1/2 ΔFt=W cos θA±μFn[+ for upward motion, − for downward motion]ΔM=μFnr 
Where:
Fn=net normal force acting on the section, lb-ft (N-m)
Ft=axial tension acting at the lower end of the section, lb-ft (N-m)
ΔFt=increase in tension over the length of section, lb-ft (N-m)
ΔM=increase in torsion over the length of section, ft-lb (N-m)
r=characteristic radius of the section, ft (m)
W=buoyed weight of the section, lb (N)
Δα=increase in azimuth angle over length of the section, degrees (rad)
Δθ=increase in inclination angle over length of section, degrees (rad)
θA=average inclination angle of section, degrees (rad)
μ=sliding coefficient of friction between drill string and borehole
The calculations start at the surface with an initial rotary speed of 0 rpm. The software uses the static friction coefficient when the pipe is stationary, and the sliding friction coefficient when it is moving relative to the borehole (sliding and/or rotating.). Normally the static friction is higher than the sliding friction. Next, the software calculates the torsional deflection in each section as a result of the incremental torque, ΔM, based on the mechanical properties of the section. The section properties depend on the outside and inside diameters of the section and its material density. These define the mass of the section and the rotational inertia of each section. If the sum of the incremental torques necessary to overcome the drag is greater than the torque applied to the drill string, at the surface, then the drill bit will “stick.” The software then determines what values of WOB and drill string RPM, will result in stick-slip.
In addition, the software calculates the rotary inertia—that is, the incremental time it will take each section to deflect by that amount based on the mechanical properties of the section, in particular, the inside and outside diameter of the section and its mass, the applied torque and friction. The sum of these time increments over the length of the drill string represents the change in the instantaneous speed of the drill string, which is reported to operating personal for use, for example, in operating a rotary steerable tool or ensuring that the operating conditions are not damaging the drill bit.
While such predictions of resonant frequencies, mode shapes and stick slip provided in the past, as discussed above, can aid the operator in identifying those values of the drilling parameters, such as drill string RPM and WOB, to be avoided in order to avoid excessive vibration, they do not make use of real-time data as the drilling progresses nor adequately account for changes in drilling conditions over time. Neither do they provide methods for mitigating poor drilling performance, especially vibration-related losses in drilling performance, or for optimizing drilling efficiency, or for determining the remaining fatigue life of critical components. Their usefulness is, therefore, limited.
An ongoing need therefore exists for a system and method for providing the drill rig operator with accurate information concerning vibration based on actual operating data that will allow optimum performance and tool life.